中文摘要：

这份报纸在其解决方案 polynomially 至多成长的切换的政体下面考虑一个给定的中立功能的系统。系统能容忍如果系统服从于另一环境噪音，保存多项式生长的 Brownian 噪音和颜色噪音吗？答案是积极的。这份报纸一起显示那环境噪音和政体切换工作让其答案 polynomially 至多成长的原来的中立微分系统成为答案的一个新中立功能的微分系统将仍然保存多项式生长。这显示这个中立功能的微分系统能容忍没有失去多项式生长的性质的小噪音，它暗示坚韧性。这份报纸也证明标准对作为功能的系统的一种特殊情况的中立延期系统合适。最后，二个例子被给说明主要理论。

英文摘要：

This paper considers a given neutral functional system under regime switching whose solution grows at most polynomially. Can the system tolerate Brownian noise and colour noise to preserve the polynomial growth if the system is subject to another environment noise？ The answer is positive. This paper shows that environmental noise and regime switching work together to make the original neutral differential system whose solution grows at most polynomially become a new neutral functional differential system whose solution will still preserve polynomial growth. This indicates that this neutral functional differential system can tolerate small noise without losing the property of polynomial growth, which implies robustness. This paper also proves that the criterion is suitable to neutral delay system which is as a special case of functional system. Finally, two examples are given to illustrate the main theory.